GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Mar 2019, 15:58

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If P^2 + Q^2 =1, is P – Q =1?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
Joined: 27 Apr 2012
Posts: 57
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
GMAT ToolKit User Premium Member
If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 25 Aug 2012, 05:32
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (01:47) correct 61% (01:49) wrong based on 119 sessions

HideShow timer Statistics

If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1
(2) P is a positive integer.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53792
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 25 Aug 2012, 05:41
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post Updated on: 25 Aug 2012, 05:57
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.


Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.


Originally posted by EvaJager on 25 Aug 2012, 05:52.
Last edited by EvaJager on 25 Aug 2012, 05:57, edited 1 time in total.
Manager
Manager
avatar
Joined: 27 Apr 2012
Posts: 57
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
GMAT ToolKit User Premium Member
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 25 Aug 2012, 05:56
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 25 Aug 2012, 06:01
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.


No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from \(P^2+Q^2=1\)).
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53792
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 25 Aug 2012, 06:04
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.


Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 --> Q=0.

EvaJager wrote:
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.


Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.


If the first statement were P-Q=1, then it would be sufficient, since that's exactly what we are asked - to find whether P-Q=1.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 25 Aug 2012, 06:15
Bunuel wrote:
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.


Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 --> Q=0.

EvaJager wrote:
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.


Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.


If the first statement were P-Q=1, then it would be sufficient, since that's exactly what we are asked - to find whether P-Q=1.


OMG...I'm an astronaut today...
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 17 Dec 2012
Posts: 1
Concentration: Marketing, Strategy
Schools: Darden '14
GPA: 3.6
WE: Analyst (Telecommunications)
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 21 Oct 2013, 11:46
EvaJager wrote:
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.


No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from \(P^2+Q^2=1\)).


hi,
not sure, if iota (i) concept can be applied in here ..

i thought, in verifying S2,
P=2, Q^2=-3, Q=sqrt3 * iota
so, in this case also, p^2+Q^2=1
Manager
Manager
avatar
B
Joined: 07 May 2015
Posts: 79
GMAT ToolKit User
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 06 Feb 2016, 13:17
Hi Bunuel

Can you please tell me why A cant be sufficient using below approach?

Given P^2 + Q^2 = 1.

P-Q = 1 => SQUARING BOTH SIDES => P^2 + Q^2 -2PQ = 1
=> 1 -2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So our question becomes whether one of p or q is zero?

Now looking at A :

P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So this should be sufficient right?

Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53792
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 07 Feb 2016, 04:34
neeraj609 wrote:
Hi Bunuel

Can you please tell me why A cant be sufficient using below approach?

Given P^2 + Q^2 = 1.

P-Q = 1 => SQUARING BOTH SIDES => P^2 + Q^2 -2PQ = 1
=> 1 -2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So our question becomes whether one of p or q is zero?

Now looking at A :

P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So this should be sufficient right?

Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.


You cannot square. If p - q = -1, then (p - q)^2 would be equal to 1^2 but p - q = -1 is not equal to 1.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 28 Jan 2019
Posts: 1
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

Show Tags

New post 16 Mar 2019, 04:39
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.


Hi, Any reason why we shouldn't rephrase the question ?

P-Q=1? => squaring both the sides => p^2+q^2-2pq=1 => since P^2 +Q^2 =1 => 2pq=0 => pq =0 ?????
GMAT Club Bot
Re: If P^2 + Q^2 =1, is P – Q =1?   [#permalink] 16 Mar 2019, 04:39
Display posts from previous: Sort by

If P^2 + Q^2 =1, is P – Q =1?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.